KVPY Government Jobs Exams

Let a b cr r r , , be three vectors in the xyz space such that a ×b = b × c = c × a ≠ 0 r r r r r r If A, B, C are points with
position vectors a b cr r r , , respectively, then the number of possible positions of the centroid of triangle ABC is

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KVPY Other Question

Two players play the following game : A writes 3, 5, 6 on three different cards ; B writes 8, 9, 10 on three
different cards. Both draw randomly two cards from their collections. Then A computes the product of two
numbers he/she has drawn, and B computes the sum of two numbers he/she has drawn. The player getting the
larger number wins. What is the probability that A wins ? The sum of (1^2 – 1 + 1)(1!) + (2^2 – 2 + 1)(2!) + …. + (n^2 – n + 1)(n!) is